 | Arthur Schultze - 1901 - 392 σελίδες
...(124) (101) But both of the above consequences would contradict the hypothesis. .-. AC> AB. 126. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. 127. NOTE. — The method used in the above proof is known as the "indirect method" or... | |
 | International Correspondence Schools - 1901 - 578 σελίδες
...one-half of the semi-circumference AD /», and one-half a semi-circumference is a quadrant (Art. 9). 24. The shortest line that can be drawn from a point to a line is the perpendicular from that point to the line. Thus, in Fig. 13, PQ is perpendicular to the... | |
 | John Alton Avery - 1903 - 136 σελίδες
...angles opposite them are unequal, the greater angle being opposite the greater side. 81. Theorem XXX. A perpendicular is the shortest line that can be drawn from a point to a line. 82. Corollary. The shortest distance from a point to a line is the perpendicular from the point... | |
 | Charles Godfrey, Arthur Warry Siddons - 1903 - 384 σελίδες
...other st. line drawn from O to meet AB. .'. ON is the shortest of all such lines. QE J i. NOTE. Since the perpendicular is the shortest line that can be drawn from a given point to a given line, it is called the distance of the point from the line, Ex.668. In fig.... | |
 | George Clinton Shutts - 1904 - 112 σελίδες
...Zj& 3 and 4. 2. Compare lines AB and A C. Give auth. Therefore — PROPOSITION XXXVI. 130. Theorem. A perpendicular is the shortest line that can be drawn from a point to a straight line. A -D MB Let AB represent the shortest line from A to the line CD. To prove that AB is perpendicular... | |
 | Fletcher Durell - 1904 - 232 σελίδες
...straight line passing through the center of the circle and perpendicular to its plane. 521. COK. 3. The perpendicular is the shortest line that can be drawn from a given point to a given plane. 522. DEF. The distance from a point to a plane is the perpendicular drawn... | |
 | Fletcher Durell - 1904 - 382 σελίδες
...(</ equals be subtracted from unequals, the remainders are unequal in the same order}. QED 94. COR. The perpendicular is the shortest line that can be drawn from a given point to a given line. For, in the Fig. page 31, PP'<PR + RPI, Art 92. Or, 2PQ<2PR. Ax. 8. .-.... | |
 | Fletcher Durell - 1911 - 553 σελίδες
...equals l)e subtracted from unequals, the remainders are unequal in the same order). Q. s. D. 94. COR. The perpendicular is the shortest line that can ~be drawn from a given point to a given line. For, in the Fig. page 31, PP' <PR + RP, Art 92. Or, 2PQ<2PR. Ax. 8. /.... | |
 | Edward Rutledge Robbins - 1906 - 268 σελίδες
...external point it is not possible to draw three equal lines to a given straight line. 77. THEOREM. The perpendicular is the shortest line that can be drawn from a point to a straight line. Given: PR ±toAB; PC not -L. To Prove : PB < PC. Proof : Extend PR to X, making RX = PR. Draw cX. PR... | |
 | Wisconsin. Department of Public Instruction - 1906 - 124 σελίδες
...I. Two oblique lines cutting off equal distances from the foot of the perpendicular are equal. 27. The perpendicular is the shortest line that can be drawn from a point to a straight line. 28. Two equal lines drawn from a point in the perpendicular to a given line, cut off equal distances... | |
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The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP 
